What’s the perimeter of the polygon if One point is (-1,3) one point is (4,3) one point is (4,0) and one point is (-1,0) 

To find the perimeter of the polygon with the given points, we need to determine the distance between consecutive points and then sum these distances.

The points provided are:
- \( A(-1, 3) \)
- \( B(4, 3) \)
- \( C(4, 0) \)
- \( D(-1, 0) \)

These points form a rectangle because opposite sides are parallel and equal in length.

### Step 1: Calculate the distance between each pair of consecutive points.
1. **Distance between \( A(-1, 3) \) and \( B(4, 3) \):**

   Since both points have the same \( y \)-coordinate (3), the distance is simply the difference in the \( x \)-coordinates:
   \[
   AB = |4 - (-1)| = 5
   \]

2. **Distance between \( B(4, 3) \) and \( C(4, 0) \):**

   Since both points have the same \( x \)-coordinate (4), the distance is simply the difference in the \( y \)-coordinates:
   \[
   BC = |3 - 0| = 3
   \]

3. **Distance between \( C(4, 0) \) and \( D(-1, 0) \):**

   Since both points have the same \( y \)-coordinate (0), the distance is simply the difference in the \( x \)-coordinates:
   \[
   CD = |4 - (-1)| = 5
   \]

4. **Distance between \( D(-1, 0) \) and \( A(-1, 3) \):**

   Since both points have the same \( x \)-coordinate (-1), the distance is simply the difference in the \( y \)-coordinates:
   \[
   DA = |3 - 0| = 3
   \]

### Step 2: Sum the distances to find the perimeter.
\[
\text{Perimeter} = AB + BC + CD + DA = 5 + 3 + 5 + 3 = 16
\]

Thus, the perimeter of the polygon is **16 units**.

Would you like more details or have any questions?

Here are five related questions you might find interesting:
1. How would you find the area of the same polygon?
2. What if the polygon were a different shape, like a trapezoid—how would you approach the perimeter then?
3. How do you find the perimeter of a polygon with more than four sides?
4. How would the process change if the points were in 3D space instead of 2D?
5. How do you find the perimeter of a circle or an ellipse?

**Tip:** Remember, when calculating distances between points in a 2D plane, it's often easiest to check if the points are horizontally or vertically aligned to simplify your calculations.

Learn how to calculate the perimeter of a polygon with given vertices using the distance formula. This problem involves determining distances between consecutive points and summing them to find the polygon's perimeter. Suitable for students in Grades 7-9.

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